This application is based on Japanese Patent Application Nos. 11-139087 (1999) filed May 19, 1999 and 11-260816 (1999) filed Sep. 14, 1999, the contents of which are incorporated hereinto by reference.
1. Field of the Invention
The present invention relates to a method and apparatus for measuring a temporal waveform of the electric field of an optical signal, and particularly to a technique for accurately measuring temporal variations in intensity and phase of ultra-fast optical signals whose temporal waveforms cannot be measured with an ordinary means because of their much faster changes than the response time of existing high-speed optical detectors or electronic circuits. Generally, a simultaneous measuring of the intensity and phase enables full determination of the characteristics of an optical signal as a classical electromagnetic wave. Therefore, such types of measuring methods are referred to as a method for measuring a temporal waveform of the electric field of an optical signal.
2. Description of the Related Art
Ultra-fast optical signals in a picosecond to femtosecond order, which have no suitable optical detector with a sufficient time resolution, have been observed by correlators in the recent twenty years. Such correlators make an optical signal to be measured and a reference optical pulse incident and focused onto a nonlinear medium, and measure the integrated power of the generated light in terms of a function of a time relationship (delay time) between the optical signal to be measured and the reference optical pulse. In this case, the time resolution is determined only by the response time of the nonlinear medium and the width of the reference optical pulse, completely independently of the response time of an optical detector or the like for carrying out optic-electrical conversion of the generated light. Using the optical signal to be measured itself as the reference optical signal provides a simplest and versatile measuring method. The signal obtained in this measurement is called an autocorrelation signal, and the apparatus for measuring it is called an autocorrelator.
It was once considered difficult to obtain the waveform of the optical signal to be measured from the autocorrelation signal without imposing any conditions.
At the present, however, it is known that by complementing the data by the spectrum of the optical signal to be measured, an iterative calculation enables the simultaneous calculation of the intensity and phase of the optical signal to be measured. Such a method is disclosed in Japanese Patent Application Publication No. 5-2252 (1993) (Japanese Patent Application No. 61-211100 (1986) xe2x80x9cMethod for measuring and estimating ultrashort optical pulsesxe2x80x9d by Kazunori Naganuma and Juichi Noda, or U.S. Pat. No. 4,792,230 xe2x80x9cMethod and apparatus for measuring ultrashort optical pulsexe2x80x9d, by Kazunori Naganuma and Juichi Noda.
Another analogous methods are carried out which observe a spectrum of light generated in an nonlinear medium, and calculate the intensity and phase of an optical signal to be measured by performing iterative calculation using two-dimensional data of two variables, the spectrum component of the generated light and the time delay. For example, such a method is described in detail in R. Trebino, K. W. Delong, D. N. Fittinghoff, J. N. Sweetser. M. A. Krumbuegel and B. A. Richman xe2x80x9cMeasuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gatingxe2x80x9d, Review of Scientific Instrument, Vol. 68 (1997), pp. 3277-3295.
However, such methods for measuring waveforms of optical signals have an ineradicable drawback in that they cannot deal with optical signals with complicated waveforms, and hence cannot fulfill the needs of the measurement in the recent optical information processing field. For example, as a simplest example of an optical signal waveform that those methods cannot deal with, is known a pair of pulses with different phases.
Furthermore, since the iterative calculation is nonlinear, it is very difficult to estimate the effect. of noise or error in the data used for the calculation on the calculation results. In a worst case, the calculation falls into a chaotic behavior so that a slightest variation in the input can result in an entirely different output. None of the foregoing iterative calculations are guaranteed that such behavior does not take place. Thus, the quality and accuracy of measuring apparatuses based on such methods cannot be warranted because of the intrinsic ambiguity of the iterative calculation.
Let us consider here the reason why the measurement of the temporal waveform of the electric field of an optical signal requires the iterative calculation. It is well known that Fourier transform can bring any temporal waveform into one-to-one correspondence with a spectrum in a frequency domain. In other words, once a spectrum of a signal is known, its temporal waveform can be obtained by inverse Fourier transform. As for the electric field of optical signals, their power spectra are usually measured using a common optical spectrum observing method, and hence it is not difficult to obtain the magnitudes (amplitudes) of the spectra of the optical signals. However, without acquiring the phases of the spectra, the corresponding temporal waveforms cannot be obtained from the spectra using the inverse Fourier transform. Here, with the optical signals, there are circumstances that the measurement of the spectral phases is not obvious at all.
Such circumstances that although the magnitude of some physical quantity is known, its phase is difficult to obtain are often encountered in various scientific fields. Thus, to mathematically handle the circumstances, there has been established a distinct academic branch called phase retrieval problem. The foregoing iterative calculation is considered as an application of a method for a phase retrieval problem to the measurement of optical signals.
Direct observations of the spectral phase will enable temporal waveforms of electric field of optical signals to be obtained without using the iterative calculation involving the complicated phase retrieval problem. Recently, such a direct measuring method of the spectral phase has attracted attention, and some proposals have been made that can be called frequency shearing interferometer.
A classical interferometer detects in a direct current (DC) manner an interference signal that is obtained by splitting an optical signal into two waves, and by recombining and interfering them again. In this case, the spectral components of the same frequency are superimposed so that those frequencies are mutually nullified, and thus the DC component is generated. However, since the phases of the spectral components are completely canceled out at the same time, the spectral phases can never be observed. Even if a fast optical detector of today is used to observe the interference signal, because it cannot follow the ultra-fast optical signal in a picosecond to femtosecond order to be observed here, it cannot exceed the realm of the DC observation, providing only the same result.
In view of this, a frequency shearing interferometer is proposed that splits an optical signal into two portions, shifts the frequency of one of them, and recombines them to interfere with each. other. Assuming the shift amount to be xcex94xcexd, the spectral components with the frequency shift xcex94xcexd superimpose on each other to cancel out the frequency components, thereby generating a DC component. The magnitude of the DC component depends on the phase difference between the spectral components with the frequency shift xcex94xcexd. This enables the spectral phase to be directly observed in terms of the difference using xcex94xcexd as a step. The principle of such a frequency shearing interferometer is disclosed in V. Wong and I. A. Walmsley xe2x80x9cAnalysis of ultrashort pulse-shape measurement using linear interferometersxe2x80x9d, Optics Letters, Vol. 19 (1994), pp. 287-289.
If the shift amount xcex94xcexd is too small, the phase difference also becomes too small and is buried in noise, producing no significant result. Accordingly, a particular means for shifting the frequency determines the feasibility of the frequency shearing interferometer.
Using a phase modulator as the frequency shifter will be most easily conceived. The example is disclosed in J. Debuau, B. Kowalski and R. Boittin, xe2x80x9cSimple method for the complete characterization of an optical pulsexe2x80x9d, Optics Letters, Vol. 23 (1998), pp. 1784-1786. However, the frequency shift amount xcex94xcexd provided by such a method is at most the driving frequency of a modulator or twice that.
Considering the performance of current modulators, it is completely insufficient to apply them to ultra-fast optical signals in the picosecond to femtosecond order the present invention is planing to handle. Furthermore, if the frequency shift amount xcex94xcexd provided by existing electronic circuits can meet the shift amount required, this means that the optical signal is sufficiently slow so that its waveform can be directly observed without much difficulty using an ordinary means combining an existing fast optical detector with a high-speed electronic circuit. In short, using the electrical phase modulator as the frequency shifter has little practical importance.
Recently, a more innovative method that can obtain the frequency shift amount xcex94xcexd in an optical frequency domain is disclosed by C. Iaconis and I. A. Walmsley, xe2x80x9cSpectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulsesxe2x80x9d, Optics Letters, Vol. 23 (1998), pp. 792-794. It can implement a sufficient frequency shift amount even for an ultra-fast optical signal in the picosecond to femtosecond order. FIG. 13A is a schematic diagram showing a setup for implementing a conventional method for measuring a temporal waveform of the electric field of an optical signal.
In this example, an optical signal to be measured 501 is split into two portions by a beam splitter 502. One of them transmitted through a dispersive optics 516 reflects off a reflector 508, and reaches a beam combiner 511. The other of them transmitted through an optical signal pair generating optics, which consists of a half mirror 517 and a pair of reflectors 518 and 519, reaches the beam combiner 511. The two optical signals reaching the beam combiner 511 are combined, and incident and focused on a sum-frequency generation (SFG) crystal 520.
The power spectrum of the light emitted from the SFG crystal 520 is observed by an optical spectrum observation instrument 515.
The operation of the conventional system will now be outlined with reference to FIG. 13B, a schematic view of the temporal behavior of optical signals incident onto the SFG crystal 520. For the purpose of simplicity, it illustrates a case in which a simple optical pulse is supplied as the optical signal to be measured 501. First, the light transmitted through the optical signal pair generating optics and emitted from the half mirror 517 appears in the form of a pair of pulses with maintaining its original pulse width.
Assume that the time interval between the pair of pulses is xcfx84. The time interval xcfx84 can be determined by providing a difference between the optical path length from the half mirror 517 to the reflector 518 and the optical path length from the half mirror 517 to the reflector 519, and by adjusting the difference. On the other hand, the light transmitted through the dispersive optics 516 is broadened in the pulse width and varied in its instantaneous frequency with time, thus forming a pulse with chirping.
The SFG crystal 520 generally generates a sum frequency xcexd1+xcexd2 for the two optical signals with frequencies xcexd1 and xcexd2. Assuming that the power spectrum of the optical signal to be measured 501 is S(xcexd), the SFG crystal 520 outputs the optical signals having power spectra S(xcexdxe2x88x92xcexdp) and S(xcexdxe2x88x92xcexdxe2x80x2p), the power spectra translated on the frequency axis respectively corresponding to the pulse pair emitted from the half mirror as shown in FIG. 13B, where the shift amounts xcexdp and xcexdxe2x80x2p are the instantaneous frequencies of the portions that each of the pulse pair emitted from the half mirror overlaps with the pulse emitted from the dispersive optics.
The difference between the instantaneous frequencies is expressed by
xcexdxe2x80x2pxe2x88x92xcexdp=(2xcfx80D)xe2x88x921xcfx84xe2x80x83xe2x80x83(1)
where D is the second-order dispersion of the dispersive optics 516, and xcfx84 is the time interval between the pulse pair emitted from the half mirror. The frequency difference operates as the frequency shift amount xcex94xcexd in the conventional frequency shearing interferometer. For example, when selecting D=0.01 ps2 and xcfx84=0.1 ps, xcex94xcexd becomes 1.6 THz, constituting a sufficient shift amount for an optical signal in a femtosecond order.
Thus, the conventional system enables the spectral phase difference to be directly observed for the optical signal input to be measured from a picosecond to femtosecond region. Subsequent calculation of the running sum of the differences gives the spectral phase. Finally, the electric field of the optical signal can be calculated by attaching the spectral phase to the magnitude of the spectrum of the optical signal obtained from the power spectrum measured by another method, and by carrying out the inverse Fourier transform thereof. Thus, the conventional system can measure the temporal waveform of the electric field of the ultrashort optical signal without using the iteration calculation.
However, the conventional measuring method of the temporal waveform of the electric field of the optical signal described above present the following problems.
Generally speaking, there are two factors that determine the response time of a nonlinear medium (the sum-frequency generation crystal, in the conventional system).
The first factor is the response of the nonlinear polarization following to the variations in the electric field of the optical signal incident and focused on the nonlinear medium. In a non-resonant nonlinear effect without involving a real transition, the response of the nonlinear polarization corresponds to the orbiting time of electrons around a nucleus, that is, approximately 1-2 fs, in which case, this factor can be considered to exhibit an instantaneous response in practice. In contrast with this, in the non-resonant nonlinear effect involving the real transition, it is difficult to obtain sufficient responsivity for measuring the ultra-fast optical signal in the picosecond to femtosecond order because of a limitation imposed by the response time of the medium. Therefore, the temporal waveform measuring apparatus including classical autocorrelators usually employ a
The second factor relates to a phase matching. For nonlinear polarizations, which will take place in various portions in a finite length medium, to contribute to the electric field of output light in phase, it is necessary for the phases of the nonlinear polarizations to be in phase with the propagation phase of the output light. Since the phases of the nonlinear polarizations occurring in various portions are determined by the propagation phase of the input light, the condition can be reduced to the relationship between the propagation phase of the input light and that of the output light. For example, when obtaining the output light with the sum frequency xcexd3 (xcexd3=xcexd1+xcexd2)from two input light waves with the frequencies xcexd1 and xcexd2 by a sum-frequency generating crystal, the contributions of the nonlinear polarizations in various portions of the medium add up each other when the phase mismatch xcexdk given by the following expression is zero, resulting in the maximum output light.
xcexdk=k1+k2xe2x88x92k3 xe2x80x83xe2x80x83(2)
where ki are wave numbers of the light waves, which are expressed by ki =nixcfx89i/c, where ni are the refractive indices and c is the speed of light in vacuum. Using equation (2), it is found that in order to make the phase mismatch zero, that is, to establish phase matching, all three refractive indices are equal, or the refractive index associated with the maximum frequency lies in between the remaining two refractive indices.
In a wavelength region in which the medium is transparent, since the refractive index monotonically increases with the frequency, the phase matching can never be established as long as considering only a single refractive index.
An anisotropic optical medium exhibits birefringence that the refractive index varies along the direction of the electric field of light.
Applying this phenomenon makes the phase matching possible which is called angular phase matching. The refractive indices ns exhibited by light transmitted in the direction s (vector quantity) in a birefringence optical crystal with a principal refractive index (nx, ny, nz) can be obtained by solving the following Fresnel""s velocity formula.                                                         S              x              2                                                      n                S                                  -                  2                                            -                              n                x                                  -                  2                                                              +                                    S              y              2                                                      n                S                                  -                  2                                            -                              n                y                                  -                  2                                                              +                                    S              z              2                                                      n                S                                  -                  2                                            -                              n                z                                  -                  2                                                                    =        0                            (        3        )            
Generally, two refractive indices are obtained for each propagation direction. The two different refractive indices correspond to linear polarizations orthogonal to each other. To establish phase matching, it is necessary for the light wave with the maximum frequency among the three waves to be propagated with the polarization giving the low refractive index, and for one of the two remaining light waves to be propagated with the polarization giving the high refractive index. For the remaining light wave we can choose the high or low refractive index, which is called type 1 or type 2 phase matching. After selecting the combination of the polarizations of the light waves, the common propagation direction s (vector quantity) that makes zero the phase mismatch in equation (3) is searched for.
On the other hand, a quasi phase matching technique has attracted attention recently that artificially constructs a structure in which the nonlinear coefficient varies periodically, and tries to achieve the phase matching using the periodicity. The quasi phase matching can utilize, even in a nonlinear crystal like lithium niobate having been conventionally used, a larger component such as dzzz in the nonlinear coefficient tensor, which is unusable in the foregoing angular phase matching. The technique is expected to implement a higher efficient nonlinear effect, or to enable the phase matching in a wavelength region in which the angular phase matching cannot be established. Furthermore, since the polarization of the input and output light waves can be set along the principal axis of a crystal, problems generally accompanying the angular phase matching can be avoided in that the birefringence limits the interaction length and degrades the shape of the output light beam. Moreover, as for materials inapplicable to the angular phase matching, such as semiconductor or glass, the quasi phase matching opens up new possibility for establishing the phase matching with them.
To achieve the quasi phase matching, although it is ideal that the nonlinear coefficients vary sinusoidally, because of the difficulty of implementing such variations in practice, a stepwise variation in the nonlinear coefficients is used. The implementation method of the variation in the nonlinear coefficients depends on materials. For example, in a ferroelectric crystal such as lithium niobate, the structure is constructed in which the sign of the nonlinear coefficient is changed periodically by reversing the polarization by applying external electric field. As for semiconductor materials, the structure is also built in which the sign of the nonlinear coefficient is changed periodically by bonding or by epitaxial growth on a substrate with its surface state varying periodically. In glass or organic materials, the sections are intermingled in which the nonlinear coefficient is nonzero and zero using periodic thermal polarization or periodic etching process. The effective nonlinear coefficient deff involving the stepwise nonlinear coefficient variation is usually given by the following equation.
deff=(ds/xcfx80) sin (xcfx80R)xe2x80x83xe2x80x83(4)
where ds is the peak-to-peak amplitude of the nonlinear coefficient, which equals 2d when the nonlinear coefficient swings between d and xe2x88x92d because of the sign inversion, and equals d when it swings between d and zero, and where R is a ratio at which a high nonlinear coefficient portion occupies in one period. When the high and low portions of the nonlinear coefficient are repeated at 1:1, the ratio R is 1/2, offering the maximum effective nonlinear coefficient.
The variation period xcex9 of the nonlinear coefficient required for the quasi phase matching is obtained from the condition that cancels out the phase mismatch of the foregoing equation (2) by the wave number corresponding to the period, and is given by the following expression.
xcex9=2xcfx80/|k1+k2xe2x88x92k3|xe2x80x83xe2x80x83(5)
Once the variation period thus selected has been constructed, the frequencies xcexd1, xcexd2 and xcexd3, at which the phase matching is established in the nonlinear medium, are fixed. This is undesirable for the application to an instrument such as a temporal waveform measuring apparatus requiring tuning of the phase matching frequencies to the frequency of the input optical signal. This problem, however, has been solved recently by the following methods: a method of using a nonlinear medium to which fan-out poling is imposed so that the period varies in the direction perpendicular to the optical path; and a method of carrying out tuning by propagating the light in the direction having an angle with the wave number direction of the periodical structure in the nonlinear medium, and by varying the incident direction of the light to the medium.
These phase matching tuning methods are respectively disclosed by Y. Ishigame, T. Suhara and N. Nishihara, xe2x80x9cLiNbO3 waveguide second-harmonic-generation device phase matched with a fan-out domain inverted grating,xe2x80x9d Optics-Letters, Vol. 16 (1991), pp. 375-377, and Japanese Patent Application Laid-open No. 10-92981 (1998), xe2x80x9cWavelength variable quasi phase matching devicexe2x80x9d by Kazunori Naganuma, Shigeo Ishibashi, Hidetoshi Iwamura and Hirohisa Kanbara.
When the phase matching is achieved by placing the foregoing phase mismatch to zero, a bandwidth around the phase matched frequency to be considered. In the plane-wave approximation, the dependence of the power conversion efficiency to the output light on the phase mismatch xcex94k and medium length L is given by the following expression.
xcex7xe2x88x9dL2 sinc2 (xcex94kL/2)xe2x80x83xe2x80x83(6)
where the function sinc(x) represents (sin x)/x in equation (6). The value xcex94kL/2 providing the first zero of the output light intensity is equal to xcfx80. The phase mismatch xcex94k at this point is translated to the bandwidth BW (full width) of the input light by the following equation for the second harmonic generation (SHG) on which the classical autocorrelator is based;
BW=((xcfx843xe2x88x92xcfx841)L)xe2x88x921xe2x80x83xe2x80x83(7)
and for the sum frequency generation (SFG) on which the conventional system is based.
BW=2((xcfx843xe2x88x92xcfx841)L)xe2x88x921xe2x80x83xe2x80x83(8)
where xcfx841 and xcfx843 are group delays per unit length of the medium for the input light and output light. Therefore, (xcfx843xe2x88x92xcfx841)L in equations (7) and (8) represents the difference between the group delays of the input light and output light proceeding through the crystal, and hence can be called group delay mismatch. The reciprocals of the bandwidths indicate the response time of the nonlinear medium for the incident light.
As the medium length L decreases, the response time reduces. This means from different point of view that the bandwidth in terms of the input light conversion increases at the same time. However, as the medium length reduces, the conversion efficiency rapidly decreases in proportion to the square of the medium length, resulting in the reduction in the measurement sensitivity.
More rigorously, the square dependence strictly holds when the beam propagates in the medium with its diameter maintained, that is, when the medium has a channel waveguide structure. When propagating in the bulk medium, adjusting the beam diameter to an optimum value proportional to the square root of the medium length (L1/2) can alleviate the dependence of the conversion efficiency on the medium length to its first power (L). However, to measure an optical signal faster than a picosecond, both the conventional method and the classical autocorrelator method previous thereto require the medium length less than 1 mm. Hence, to focus the beam down to a smaller diameter in accordance with the medium length L less than that is not practical hence not carried out.
As described above, the non-resonant nonlinear effect, which the apparatus for measuring temporal waveform is based on, is much smaller than the resonant effect. Therefore, it is desirable that the conversion efficiency be increased as much as possible by increasing the medium length. The increase in the medium length, however, degrades the response time at the same time. Thus, there is usually a tradeoff between the sensitivity and the response time.
This will be described in more detail. First, the classical autocorrelator observes the second harmonic (SH) light generated in the nonlinear medium without spectral decomposition. Disregarding the bandwidth of the nonlinear medium, it is known that the observed signal is proportional to Ppxc2x7Pav, where Pp and Pav are peak power and average power of the optical signal to be measured. Considering that the acceptable medium length is limited in proportion to the time width tp of the optical signal because of the effect of the bandwidth, the observed signal S accords with the following expression.
Sxe2x88x9dtp2Ppxc2x7Pavxe2x80x83xe2x80x83(9)
In the conventional frequency shearing interferometer, the peak powers of the light waves with the frequencies xcexdp and xcexdxe2x80x2p are proportional to (xcex94ptp)2Pp, and it substitutes for the Pp of the above expression (9), where xcex94p is the line width of the light waves. Accordingly, when disregarding the bandwidth of the nonlinear medium, the observed signal is proportional to (xcex940tp)(xcex94ptp)2PpPav, where the factor xcex940tp reflects the fact that the generated sum frequency (SF) is observed after spectrally decomposed, and xcex940 is the resolution of the spectrum observation instrument. The xcex94p or xcex940 can be broadened as the width of the optical signal reduces.
Thus, the factors xcex940tp and xcex94ptp can be about 0.1 independently of tp, and the reduction of about 103 in the sensitivity due to them is acceptable at the cost of the direct measurement of the spectral phase. Taking account of the restriction imposed on the medium length because of the bandwidth effect, the observed signal accords with the following expression (10).
Sxe2x88x9d(xcex940tp)(xcex94ptp)2tp2 Ppxc2x7Pavxe2x80x83xe2x80x83(10)
As expressed by the foregoing expressions (9) and (10), both the conventional system and the classical autocorrelator reduce their sensitivity in accordance with the square of the temporal resolution to be achieved.
Even if such sensitivity reduction is accepted, another practical problem arises accompanying the increase in the temporal resolution. The problem is that the medium length L required becomes very thin. For example, in an angular matching lithium niobate crystal, the bandwidth given by the foregoing expression (7) equals (158 fs) xe2x88x921 per 1 mm of the crystal length for the SHG from 1.55 xcexcm. To obtain the resolution of 10 fs, a very thin crystal plate of 63 xcexcm thickness is required. It is not easy to fabricate and polish such a thin crystal plate. Furthermore, with a more efficient quasi phase matching lithium niobate crystal, the bandwidth become narrower, (299 fs)xe2x88x921 per 1 mm of the crystal length. In this case, the 10 fs resolution requires a 33 xcexcm thick crystal plate, which is very difficult to fabricate. In the SFG on which the conventional system is based, only twice the bandwidth of the SHG is obtained as seen from equation (8), which presents no ultimate solution to the problems.
Consider measuring an optical signal actually varying at a rate of 10 fs using a measuring apparatus with a nominal resolution (response time) of 10 fs described above. In this case, it is unavoidable for the classical autocorrelator to suffer an error in the measurement. In the case of the conventional frequency shearing interferometer, since the intensity of the signal becomes weak in the wings of the power spectrum translated along the frequency axis, it is difficult to measure the phase in such wings. On the other hand, currently available ultra-short pulse sources can generate pulses with a width as narrow as 10 fs or less. Thus, it is obvious that both the classical autocorrelator and the conventional frequency shearing interferometer cannot meet the requirements of the current high-speed optical signal generation and control technologies.
As described above, the conventional methods for measuring waveforms of electric field of an optical signal have the following problems:
(1) Trying to increase the temporal resolution results in the reduction in the sensitivity in proportion to the square of the resolution; and
(2) The temporal resolution currently required cannot be realized in the first place because it needs a nonlinear medium with a length impractically thin.
It is therefore an object of the present invention to provide a technique capable of measuring temporal waveforms of the electric field of a ultra-fast optical signal accurately without substantially sacrificing the sensitivity and without carrying out the iterative calculation.
The foregoing and other objects and novel features of the present invention will become apparent from the following description given in connection with the accompanying drawings.
Outlines of the typical aspects of the present invention disclosed herein will be briefly explained.
(1) According to a first aspect of the present invention, there is provided a method for measuring a temporal waveform of the electric field of an optical signal comprising the steps of: generating phase conjugated light by applying local oscillator light to optical signal to be measured; generating mixed light by combining the optical signal to be measured with the phase conjugated light; obtaining a spectral phase by observing a spectrum of the mixed light; and obtaining a temporal waveform of the electric field of the optical signal to be measured by attaching the spectral phase to a separately observed spectrum of the optical signal to be measured.
(2) The method may further comprise the step of acquiring spectra of two mixed light waves which are associated with the local oscillator light having different wavelengths.
(3) The method may further comprise the step of carrying out for each spectrum of the mixed light waves multiple times of measurements with different fixed relative phases between the local oscillator light and the optical signal to be measured.
(4) The method may further comprise the step of comparing, for each wavelength of the local oscillator light, intensity changes in at least two spectral components in the mixed light resulting from changes in a relative phase between the local oscillator light and the optical signal to be measured, and the step of measuring a relative phase between the at least two spectral components using results of the step of comparing.
(5) The step of comparing intensity changes in at least two spectral components resulting from the changes in the relative phase may comprise the steps of: changing the relative phase in a ramp (linear slope) fashion; generating, for sinusoidal intensity changes obtained, a signal whose phase is shifted by 90 degrees from a spectral component adopted as a reference; integrating a product of the intensity changes of the spectral component and intensity changes in another spectral component to obtain a first integral; integrating a product of the intensity changes of the spectral component and the signal whose phase is shifted by 90 degrees to obtain a second integral; and obtaining the relative phase between the spectral components from a ratio of the two integrals.
(6) The integration interval of the integration is set at an integer multiple of a period of the intensity changes in the spectral component adopted as the reference.
(7) The method may further comprise the steps of: splitting the optical signal to be measured; generating the local oscillator light by launching first optical signal to be measured onto a medium with a second-order optical nonlinear effect, the first optical signal to be measured being a first portion split; and generating the phase conjugated light by launching the generated local oscillator light and second optical signal to be measured onto another medium with a second-order optical nonlinear effect, the second optical signal to be measured being a second portion split.
(8) The method may further comprise the step of limiting a spectral width of the local oscillator light by inserting an optical filter in at least one of two positions before and after the medium with the second-order optical nonlinear effect to which the first optical signal to be measured is incident.
(9) The method may further comprise the step of amplifying the light to be incident to the medium with the second-order optical nonlinear effect to which the first optical signal to be measured is incident, or amplifying, when the optical filter is interposed, the light which is output from the optical filter and is to be incident to the medium.
(10) The method may further comprise the steps of:
generating the local oscillator light by launching first optical signal to be measured onto an optical filter; and
generating the phase conjugated light by launching the generated local oscillator light and second optical signal to be measured onto a medium with a third-order optical nonlinear effect.
(11) The method may further comprise the step of amplifying the local oscillator light.
(12) According to a second aspect of the present invention, there is provided an apparatus for measuring a temporal waveform of the electric field of an optical signal comprising: local oscillator light generating means for generating local oscillator light from optical signal to be measured; phase conjugated light generating means for generating phase conjugated light using the local oscillator light; means for obtaining a spectral phase by observing a spectrum of mixed light generated by combining the optical signal to be measured with the phase conjugated light; and means for obtaining a temporal waveform of the electric field of the optical signal to be measured by attaching the spectral phase to a separately observed spectrum of the optical signal to be measured.
(13) The apparatus may further comprise means for acquiring spectra of two mixed light waves which are associated with the local oscillator light having different wavelengths.
(14) The apparatus may further comprise means for carrying out for each spectrum of the mixed light waves multiple times of measurements with different relative phases between the local oscillator light and the optical signal to be measured.
(15) The apparatus may further comprise: means for simultaneously observing intensities of at least two spectral components in the mixed light; means for changing a relative phase between the local oscillator light and the optical signal to be measured; and means for measuring a relative phase between the at least two spectral components by comparing intensity changes in the at least two spectral components resulting from the changes in the relative phase.
(16) The means for simultaneously observing intensities of at least two spectral components may comprise two monochromators, a photo-detector mounted on each of the monochromators, and a beam splitter for splitting the mixed light into two portions to be supplied to the two monochromators.
(17) The means for simultaneously observing intensities of at least two spectral components may comprise a spectrograph equipped with a linear detector array.
(18) The apparatus may further comprise a beam splitter for splitting the optical signal to be measured, wherein the local oscillator light generating means may generate the local oscillator light by launching first optical signal to be measured onto a medium with a second-order optical nonlinear effect, the first optical signal to be measured being a first portion split by the beam splitter, and wherein the phase conjugated light generating means may generate the phase conjugated light by launching the local oscillator light generated by the local oscillator light generating means and second optical signal to be measured onto another medium with a second-order optical nonlinear effect, the second optical signal to be measured being a second portion split by the beam splitter.
(19) The apparatus may further comprise an optical filter inserted in at least one of two positions before and after the medium with the second-order optical nonlinear effect to which the first optical signal to be measured is incident, the optical filter being disposed for limiting a spectral width of the local oscillator light.
(20) The apparatus may further comprise an optical amplifier inserted before the medium with the second-order optical nonlinear effect to which the first optical signal to be measured is incident, or between the optical filter and the medium when the optical filter is inserted.
(21) The local oscillator light generating means may generate the local oscillator light by launching first optical signal to be measured onto an optical filter, and the phase conjugated light generating means may generate the phase conjugated light by launching the local oscillator light generated by the local oscillator light generating means and second optical signal to be measured onto a medium with a third-order optical nonlinear effect.
(22) The apparatus may further comprise an optical amplifier for amplifying the local oscillator light.
Thus, the essence of the present invention is summarized to the following steps: generating phase conjugated light under the action of the local oscillator light on the optical signal to be measured; observing the mixed spectrum generated as a result of combining the optical signal to be measured with the phase conjugated light; obtaining the spectral phase from the mixed spectrum; and obtaining the temporal waveforms of the electric field of the optical signal to be measured by attaching the spectral phase to the separately measured spectrum of the optical signal to be measured.
Here, since the spectral phase is obtained in the symmetrized manner with respect to the degenerate frequency, where the phase conjugated light has the same frequency as its original light, it is preferable for recovering the general spectral phase to acquire two mixed spectra with changing the wavelength or frequency of the local oscillator light.
It is also preferable for accurately detecting the spectral phase when it is small to acquire the mixed spectra multiple times with changing the fixed relative phase between the local oscillator light and the light to be measured. Alternatively, to accurately detect the very small spectral phase, a configuration can be implemented in which intensities of at least two spectral components in the mixed spectrum are observed simultaneously, and the means for changing the relative phase is provided so that the relative phase can be measured by comparing the changes in the intensities of the at least two spectral components following the changes in the relative phase.
As a method for obtaining the local oscillator light, the light to be measured can be split into two portions, followed by launching one of the portions onto the medium with the second-order optical nonlinear effect to generate second harmonic light to be used as the local oscillator light. In this case, the local oscillator light and the remaining portion of the light to be measured that is split are incident onto another medium with the second-order optical nonlinear effect to generate the phase conjugated light.
The optical filter can be interposed before and/or after the first medium with the second-order optical nonlinear effect to limit the spectral bandwidth of the local oscillator light.
Furthermore, the optical amplifier can be interposed before the first medium with the optical nonlinear effect to enhance the intensity of the local oscillator light. When the optical filter is inserted before the first medium with the second-order optical nonlinear effect, the optical amplifier is preferably located between the optical filter and the medium.
As another method of obtaining the local oscillator light, the light to be measured can be split into two portions, followed by launching one of the portions onto the optical filter to limit its bandwidth, and the output light of the optical filter can be used as the local oscillator light. In this case, the local oscillator light and the remaining portion of the light to be measured that is split are incident onto a medium with the third-order optical nonlinear effect to generate the phase conjugated light.
In either of the two methods of obtaining the local oscillator light, the optical amplifier can be inserted to intensify the local oscillator light.
The fundamental idea of the present invention is to construct a novel method for measuring a temporal waveform of the electric field of an optical signal on the basis of the optical nonlinear effect determined by the phase matching condition different from that of the conventional techniques. As the optical nonlinear effect, the inventor of the present invention pays attention to parametric mixing and four-wave mixing. These effects have in common a function to generate a phase conjugated light for the optical signal to be measured.
First, the parametric mixing will be considered. It is an effect corresponding to the reverse process of the sum frequency generation, so to speak. Under the presence of local oscillator light with a frequency v 3, there takes place mixing between any pair of light waves with frequencies xcexd1 and xcexd2 satisfying the relationship xcexd1+xcexd2=xcexd3. The two frequencies to be mixed are equal when xcexd1=xcexd2=xcexd3/2, which is called a degenerate frequency.
Defining the power conversion efficiency as the ratio of the power of the second light generated to the first light, the foregoing expression (6) holds using the phase mismatch xcex94k in the foregoing expression (2) when the light with the frequency xcexd3 is not extremely strong. As in the foregoing, the phase mismatch xcex94k, which gives the first zero point of the efficiency, is translated into the bandwidth (full width) BW of the input light xcexd1 in the neighborhood of the degenerate frequency xcexdp, which is given by the following equation.
BW=(xcfx80DL/2)xc2xdxe2x80x83xe2x80x83(11)
where D is a second-order dispersion per unit length of the medium at the degenerate frequency. The dispersion is one order higher than the group delay appearing in the foregoing expressions (7) and (8). Accordingly, the effect of the dispersion here is usually small, providing much broader phase matching bandwidth for the same length medium than the conventional system. In addition, notice that the medium length L appears here in the form of Lxe2x88x92xc2xd rather than Lxe2x88x921 as in the conventional system.
The difference, which is a natural consequence of the difference in the order of the dispersion, will alleviate the narrowing of the phase matching bandwidth with an increase in the medium length as compared with the conventional system. Thus, because of the foregoing two effects, using the parametric mixing will facilitate implementing such a wide bandwidth, that is, a high temporal resolution as the conventional system cannot accomplish.
Next, the four-wave mixing will be described. It launches the local oscillator light with a degenerate frequency xcexdp instead of the local oscillator light with the frequency xcexd3. In this case, let us redefine the phase mismatch xcex94k as follows:
xcex94k=k1+k2xe2x88x922kpxe2x80x83xe2x80x83(12)
Then, the power conversion efficiency expression of the foregoing equation (6) holds without change when the light with the frequency xcexdp is not very intense, so that the bandwidth agrees with the foregoing expression (11). Accordingly, the four-wave mixing can also achieve the same effect as the parametric mixing.
As for the parametric mixing and the four-wave mixing themselves, many researches and reports have been made already, and hence the present invention is not original in this point. However, applying the generated phase conjugated light to measuring waveforms of some optical signals, such as waveforms of electric field or of intensity, has not been reported until now. This is because the phase conjugated light generation up to now employs as an energy source a pump light source independent of the optical signal to be measured. Thus, the phase of the phase conjugated light is statistically completely uncorrelated with the phase of the optical signal to be measured, which does not make possible the observation of the spectral phase.
The foregoing discussion shows that to accomplish the object of the present invention, it is essential to obtain and operate the local oscillator light whose phase is fixed or very slowly varied with respect to the optical signal to be measured.
Typical advantages of the present invention are as follows:
(1) It can substantially improve the sensitivity without requiring a very thin nonlinear medium.
(2) It can measure complex temporal waveforms of the electric field of a ultra-fast optical signal very accurately without using the iterative calculation.
(3) There are two setups based on the parametric mixing and the four-wave mixing: the former can cover a wide wavelength range and measure extremely fast signals; and the latter can be configured more simply and at a lower cost.
(4) Introducing an optical amplifier as needed makes it possible to increase the sensitivity. In addition, it is guaranteed in principle that the optical amplifier does not impair the measurement accuracy.
(5) There are two setups: a first setup conducts multiple times of spectrum acquisitions using an ordinary spectroscopic instrument; and a second setup simultaneously observes the intensity of at least two spectral components, and directly measures the relative phase between the components. The former can utilize the existing spectroscopic instrument, and hence can be implemented at a lower cost. The latter can conduct a highly reliable measurement because it has strong tolerance against the fluctuations in the intensity or polarization of the optical signals to be measured. Since it does not require any particularly stable interferometer, it is used in poor environments with maintaining its performance for a long time. In addition, adopting multi-channel photometry using a linear detector array in the latter setup will implement quick measurement.
(6) Selecting a setup from these plentiful options in accordance with its object can cope with the wide measurement needs, offering great industrial advantages.